Integrated circuits for telecommunications at radio frequencies are now even more sophisticated, and require, in particular, a good PSRR (Power Supply Rejection Ratio) and voltage reference sources that are nearly independent from noise and fluctuation of the supply voltage of the circuit.
Stable voltage references are generated by bandgap voltage generators that are substantially formed by connecting components among them to compensate the effects of fluctuation of the supply voltage and variations of the operating temperature of the device.
A typical bandgap voltage generator is depicted in FIG. 1. The functioning of this generator is well known and will not be explained in detail. According to common practice, the area n*A of the output transistor Q1 of the current mirror is “n” times the area A of the input transistor Q2, and the area A′ of the feedback transistor Q3 of the bandgap voltage generator isA′=A*(IQ3/IC)  (1)where IQ3 is the current flowing through the feedback transistor Q3.
By dimensioning the transistor Q3, its base-emitter voltage VBE3 coincides with the base-emitter voltage VBE2 of the transistor Q2. Therefore, the collector of the output transistor Q1 of the current mirror is kept indirectly at the same potential of the collector of the input transistor Q2 of the current mirror.
In certain applications a very low noise reference voltage is required. The expression “low noise” means not only “low noise at high frequency” but also “low noise at low frequency”.
U.S. Pat. No. 6,462,526 discloses an architecture of a bandgap voltage generator having additional bipolar transistors for diverting part of the current flowing in the matched transistors of the voltage generator. The proposed architecture has good noise rejection figures, but the noise bandwidth at low frequency is relatively large.
Noise at high frequency may be easily filtered by using common integrated components, but it is much more difficult to curb low frequency noise. This kind of noise may significantly depress performances of certain high frequency circuits biased by the bandgap voltage generator, such as oscillators, mixers and other circuits. These circuits have nonlinear characteristics and therefore the input noise is likely to be folded or added back on the output band. In particular, nonlinear RF circuits need noise free voltage generators because input low frequency noise is added to frequency ranges in which carriers of signals to be transmitted/received normally belong.
For these reasons bandgap voltage bias generators with extremely low noise at ultra low frequencies (<100 Hz) are needed by manufacturers of oscillators and mixers for enhancing global performances of these circuits, such as spectral purity, and residual noise corruption of down-converted or up-converted signals.
FIG. 2 shows the same bandgap voltage generator of FIG. 1 in which noise sources have been indicated; {overscore (v*)}2 is the voltage noise source of the resistor R*, and {overscore (vin)}2 and {overscore (iin)}2 are noise voltage and current sources of the bandgap generator at the emitter of Q1, respectively.
An equivalent circuit to that of FIG. 2 is depicted in FIG. 3, wherein the transistor Q4 replaces the current generator Ibias, and the equivalent noise current generator {overscore (ieq)}2 is equivalent to the three noise generators {overscore (v*)}2, {overscore (vin)}2 and {overscore (iin)}2 of FIG. 2.
The power density of the noise corrupting the output voltage VBG is thus
                                          v            nBG            2                    _                =                                            i              eq              2                        _                    ·                                    (                                                R                  *                                                                      R                    *                                    +                                      1                                          gm                      Q1                                                                                  )                        2                    ·                      R            C            2                    ·                                    (                              1                                                                            V                      T                                                              V                      AQ3                                                        +                                                            V                      T                                                              V                      AQ4                                                                                  )                        2                    ·                      1                          H              r              2                                                          (        2        )            wherein gmQ1 is the transconductance of the transistor Q1, VT is the thermal voltage, VAQ3 and VAQ4 are the respective Early voltages of the transistors Q3 and Q4, and Hr is the open loop gain of the voltage generator.
By substituting {overscore (ieq)}2 with its value as a function of {overscore (vin)}2 and {overscore (iin)}2 assuming that the noise sources are uncorrelated, eq. (2) becomes
                                          v            nBG            2                    _                =                              (                                                            4                  ⁢                  k                  ⁢                                                                          ⁢                                      T                    ·                    Δ                                    ⁢                                                                          ⁢                  f                                                  R                  *                                            +                                                                                          v                                              i                        ⁢                                                                                                  ⁢                        n                                                              _                                    2                                                  R                                      *                    2                                                              +                                                i                                      i                    ⁢                                                                                  ⁢                    n                                    2                                _                                      )                    ·                                    (                                                R                  *                                                                      R                    *                                    +                                      1                                          gm                      Q1                                                                                  )                        2                    ·                      R            C            2                    ·                                    (                              1                                                                            V                      T                                                              V                      AQ3                                                        +                                                            V                      T                                                              V                      AQ4                                                                                  )                        2                    ·                      1                          H              r              2                                                          (        3        )            wherein k is Boltzmann's constant, T is the temperature of the bandgap voltage generator, and Δf is a frequency interval.
The ratio RC/R* is fixed, thus the bandgap noise voltage decreases when R* decreases, or in other words, when the bandgap current IC increases. This assumption is valid as long as the current shot noise of transistors is negligible. For this reason, very often the transistors Q1 and Q2 are designed for having high collector currents IC for reducing the output noise corrupting the voltage reference VBG.
The noise bandwidth is determined by the noise filtering capacitor CC and the equivalent resistance RCc seen from the nodes of the capacitor CC. The resistance RCc is given by the following formula
                              R          Cc                ≅                              (                                          r                                  0                  ⁢                  Q3                                            //                              r                                  0                  ⁢                  Q4                                                      )                    ·                      1                          H              r                                                          (        4        )            wherein r0Q3 and r0Q4 are the respective output resistances of transistors Q3 and Q4. Thus
                              R          Cc                ≅                              1                          I                              Q3                ,                bias                                              ·                      1                                          1                                  V                  AQ3                                            +                              1                                  V                  AQ4                                                              ·                      1                          H              r                                                          (        5        )            where IQ3=Ibias is the current flowing through the transistor Q3.
The noise bandwidth is
                              f          n                =                  1                      2            ⁢                          π              ·                              1                                  I                                      Q3                    ,                    bias                                                              ·                              1                                                      1                                          V                      AQ3                                                        +                                      1                                          V                      AQ4                                                                                  ·                              1                                  H                  r                                            ·                              C                C                                                                        (        6        )            Looking at this equation, it is clear that the noise bandwidth is reduced by keeping the current IQ3=Ibias as small as possible.
The transistors Q3 and Q2 are matched according to eq. (1) and a small bias would imply: a small bandgap current IC, which ideally should be as large as possible for reducing noise intensity; or a small current ratio IQ3/IC, which means using transistors Q1 and Q2 with very large emitters. However, it is very difficult to ensure a good match between transistors Q2 and Q3 when the area ratio A/A′ is very large.